I agree with KayTy on this. I own a horse that would pop up when I got him (usually when I asked him to stop, which might be easier to manage than a horse that rears when you ask them to go forward) and the minute he goes up high and/or he even thinks of going over on me is the same time I find a big old hole for him. Find a professional trainer (its going to cost money) and work with them. There could be a multitude of sins going on and its hard to say which is the trigger. On the ground help with someone familiar with this problem would be the best. I know this is hard to hear but no horse is worth dying over. It doesn't sound like you have to do much to get this mare up. I know you have horse experience and this is not a statement about you as a rider. Its about this horse and you are not safe.
The problem with a horse that flips is that its willing to give up its feet (ie fall vulnerable to the ground) which is something that in the wild is bad and not done.